Hey @alexgamer_hameowlton,
It is completely understandable to feel/have felt a roller coaster of emotions for jumping quickly into conclusions and realizing that it was a mistake. We learn from our mistakes though, as uncomfortable as it is. In this situation, it is easier for those who would read your post to see some silver linings in this situation, so I hope this could help you a little more to process what happened and be confident with the fact that you are now more in control of what could happen from now on.
1/ Your reaction shows how much you care, how much ethics are important to you and you hold high standards for the people you care about. It also shows that you are willing to step in and share your voice if something objectively wrong happens: it is a strong trait of your character, and not something to be ashamed of at all. If your friend would have actually done this, you would have called them out and dared to care. In a world where people are often afraid to say that something is wrong, it is truly a strength to be ready to acknowledge something unfair happening.
2/ Your friend and you have obviously a solid friendship - hurt is present, but it is also met with understanding, which is absolutely beautiful and admirable. You both seem to know each other very well and truly care for each other. That’s why the hurt/disappointment is there, that’s why you jumped into conclusions too quickly, and that’s why communication is still possible today despite all of it. There is a beautiful opportunity there to heal together from what happened, because there is mutual understanding. That’s extremely precious.
3/ You have acknowledged your mistake and apologized to her. Once again: not everyone would have done that! Far from it. It takes a lot of strength and care to say “I’m sorry, I was in the wrong”. It shows humility and a real willingness to grow from what happened. So if guilt is present regarding your first reaction, I hope you know that at least you can get rid of any potential shame.
4/ No doubt this will be an experience that you keep in mind in case that kind of thing happens in the future, so you would add more steps and time between hearing about something that strikes a chord in you and acting out of that feeling.
We learn from our mistakes, and sometimes we have no choice but to embrace them as we can. It’s very uncomfortable, but you have a beautiful context there to learn and create some restoration with your friend, little by little. There’s a before and an after, yet the “after” here holds a real potential to be met with growth, patience, healing and love.
Well done for acknowledging this mistake - “I made a horrible mistake”, as you have said, is so different from believing that you would be a horrible person. Being aware of this is a real strength. I 100% believe in you, in your thoughtfulness and your ability to grow from what happened. Your heart is big. Sometimes you might just encounter situations during which your personal limits and values are affected, and learn ways to deal with how it makes you feel personally without giving up on genuine care and dialogue.
You bring a lot of light into this world. Thank you for caring as you do. Make sure to give yourself some grace. 
You’ve been friends for 5 years, I’m sure that you can fix this and you’ll have a good friendship again